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8 identical machines, working alone and at their constant rates, take [#permalink]
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23 Aug 2015, 21:50
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8 identical machines, working alone and at their constant rates, take [#permalink]
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23 Aug 2015, 22:08
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Bunuel wrote: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?
A. 2.25 hours B. 8.75 hours C. 12 hours D. 14.25 hours E. 16 hours Ans: E Solution: 8 machines take 6 hrs to complete the job, so one machine will take 8*6= 48 hrs to complete the job alone. three machine together will finish the work in = 48/3 = 16 hrs.
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Re: 8 identical machines, working alone and at their constant rates, take [#permalink]
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24 Aug 2015, 00:16
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Bunuel wrote: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?
A. 2.25 hours B. 8.75 hours C. 12 hours D. 14.25 hours E. 16 hours
Kudos for a correct solution. IMO: E Let each machine do 1 unit of work for 1 hour 8 machines > 8 units of work in 1 hour For 6 hours = 8*6 = 48 Units of total work is done. Now this 48 Units of total work must be done by 3 machines 3 units of work(3 machines) > 1 hour for 48 Units of work 3*16 > 1*16 hours Thus a total of 16 hours
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Re: 8 identical machines, working alone and at their constant rates, take [#permalink]
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24 Aug 2015, 01:10
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8 machines take 6 hours for 1 job. Therefore their rate is 1/6. Divide by number of machines 8, and then multiply by 3 to get the rate for 3 machines.
=> \(1/6 * 1/8 = 1/48\) => \(1/48 * 3 = 3/48\)
Take the reciprocal for the time taken, 48/3 = 16 Hours



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Re: 8 identical machines, working alone and at their constant rates, take [#permalink]
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24 Aug 2015, 01:43
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Bunuel wrote: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?
A. 2.25 hours B. 8.75 hours C. 12 hours D. 14.25 hours E. 16 hours
Kudos for a correct solution. As number of machines reduced it will take more time to complete the same job. we have to increase the number of hours. multiply 6 hours with the increasing ratio, that is, 8/3 You get 16 hours.



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8 identical machines, working alone and at their constant rates, take [#permalink]
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25 Aug 2015, 13:42
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By using formula M1D1H1/w1=M2D2H2/w2 we can deduce 8*6 =3*H2 Therefore H2=16 E



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8 identical machines, working alone and at their constant rates, take [#permalink]
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25 Aug 2015, 16:33
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Bunuel wrote: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?
A. 2.25 hours B. 8.75 hours C. 12 hours D. 14.25 hours E. 16 hours
Kudos for a correct solution. A, B and C are out automatically since the number of machines are less than half, and less than half results in more than double the time. Between D and E, option E, for 16 hours is the same amount of hours (48) as the whole 8 needed. Option E. Kr, Mejia



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Re: 8 identical machines, working alone and at their constant rates, take [#permalink]
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27 Aug 2015, 07:14
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Bunuel wrote: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?
A. 2.25 hours B. 8.75 hours C. 12 hours D. 14.25 hours E. 16 hours
Kudos for a correct solution. Using chain rule, (8 machines*6 hours)/1 job done=(3 machines*no of hours)/1 job done No of hours=16 hours Answer E



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Re: 8 identical machines, working alone and at their constant rates, take [#permalink]
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30 Aug 2015, 07:45
Bunuel wrote: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?
A. 2.25 hours B. 8.75 hours C. 12 hours D. 14.25 hours E. 16 hours
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:Given that 8 machine rates = 1 job / 6 hours, you can divide both sides of that equation by 8 to find the rate of 1 machine working alone. That means that the rate of one machine is 1 job / 48 hours. Because you have 3 machines, you can multiply that rate by 3 to find the rate of 3 machines, which is then 3 jobs / 48 hours which reduces to 1 job / 16 hours. Therefore it will take 16 hours for 3 machines to perform the job. A helpful shortcut to this problem is to recognize that the time and the number of machines are inversely proportional (fewer machines will take longer). So since you have 3/8 as many machines, it will take 8/3 as long. 8/3 * 6 = 16, answer choice E.
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Re: 8 identical machines, working alone and at their constant rates, take [#permalink]
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16 Sep 2017, 06:36
Time taken by each machine = 8*1/x = 1/6 . This gives x= 48 hours. Time taken by 3 machines = 48/3 = 16 hours (E)



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Re: 8 identical machines, working alone and at their constant rates, take [#permalink]
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21 Sep 2017, 13:59
Bunuel wrote: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 3 such machines to perform the same job?
A. 2.25 hours B. 8.75 hours C. 12 hours D. 14.25 hours E. 16 hours The rate for 8 machines is 1/6. Let’s use the following proportion to determine the rate (which we can call n) of 3 machines: 8/(1/6) = 3/n 48 = 3/n 48n = 3 n = 3/48 = 1/16 We see that the rate of 3 machines is 1/16; thus, it will take 3 machines 16 hours to perform the same job. Answer: E
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8 identical machines, working alone and at their constant rates, take [#permalink]
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08 Nov 2017, 21:37
8 machines perform 1 job in 6 hours 1 machine performs \(\frac{1}{8}\) th of the job in 6 hours 1 machine performs \(\frac{1}{(8*6)}\) job in 1 hour Hence rate of 1 machine is \(\frac{1}{48}\) Rate of 3 machines is \(3*\frac{1}{48}\) = \(\frac{1}{16}\) or, 3 machines will finish 1 job in 16 hours.
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